do nothing #1 can wiggle his ears 10 more times per minute than do nothing #2 can. If the two keep wiggling their ears for five minutes straight, they will have wiggled a combined total of 550 times. How many times can do nothing #2 wiggle his ears per minute?
Let's say the rate at which do nothing #2 can wiggle his ears per minute is x.
Therefore, the rate at which do nothing #1 can wiggle his ears per minute is x + 10.
If they both wiggle their ears for 5 minutes straight, do nothing #1 wiggles his ears 5 * (x + 10) = 5x + 50 times.
The total number of times they wiggle their ears if they keep wiggling for five minutes straight is 550.
5x + 50 + x * 5 = 550
5x + 50 + 5x = 550
10x + 50 = 550
10x = 550 - 50
10x = 500
x = 500/10
x = <<50=50>>50
Do nothing #2 can wiggle his ears 50 times per minute. Answer: \boxed{50}.